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Deep neural networks (DNNs) are being increasingly used to make predictions from functional magnetic resonance imaging (fMRI) data. However, they are widely seen as uninterpretable "black boxes", as it can be difficult to discover what input information is used by the DNN in the process, something important in both cognitive neuroscience and clinical applications. A saliency map is a common approach for producing interpretable visualizations of the relative importance of input features for a prediction. However, methods for creating maps often fail due to DNNs being sensitive to input noise, or by focusing too much on the input and too little on the model. It is also challenging to evaluate how well saliency maps correspond to the truly relevant input information, as ground truth is not always available. In this paper, we review a variety of methods for producing gradient-based saliency maps, and present a new adversarial training method we developed to make DNNs robust to input noise, with the goal of improving interpretability. We introduce two quantitative evaluation procedures for saliency map methods in fMRI, applicable whenever a DNN or linear model is being trained to decode some information from imaging data. We evaluate the procedures using a synthetic dataset where the complex activation structure is known, and on saliency maps produced for DNN and linear models for task decoding in the Human Connectome Project (HCP) dataset. Our key finding is that saliency maps produced with different methods vary widely in interpretability, in both in synthetic and HCP fMRI data. Strikingly, even when DNN and linear models decode at comparable levels of performance, DNN saliency maps score higher on interpretability than linear model saliency maps (derived via weights or gradient). Finally, saliency maps produced with our adversarial training method outperform those from other methods.